Cogito
Trigonometry · Chapter 6 · Lesson 1
Compound and Double Angles
Sine does not distribute.
10 problems · about 21 minutes · F-TF.C.9
What this lesson teaches
The student applies the sum, difference, and double angle formulas.
- sin(A + B) is not sin A + sin B.
- sin(A + B) = sin A cos B + cos A sin B.
- Setting B = A gives the double angle formulas.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
2 problemsReview — Even, Odd, and Cofunction Identities: sin θ = 0.9. What is sin(−θ)?
Answer -0.9
Why −0.9.
Review — Proving an Identity: What is sin²θ + cos²θ for any angle?
Answer 1
Why 1.
Warm Up
Straightforward practice. Get the method working first.
4 problemssin A = 0.5 and cos A = 0.866. What is sin 2A, to two places?
Answer 0.87
Why About 0.87.
Why is sin(A + B) not sin A + sin B?
Answer Sine is a function, not a multiplier, so it does not distribute.
Why Functions do not distribute over addition.
sin A = 0.8, cos A = 0.6. What is sin 2A?
Answer 0.96
Why 2 × 0.8 × 0.6.
cos A = 0.6, sin A = 0.8. What is cos 2A?
Answer -0.28
Why 0.36 − 0.64.
Build It Up
The same ideas with more to keep track of.
2 problemsIs sin(A + B) equal to sin A + sin B?
Answer No.
Why Test with 90° and 90°.
What is sin 90° + sin 90°?
Answer 2
Why 1 + 1.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Test: What is sin 180°?
Answer 0
Why 0.
The Double: sin A = 0.6 and cos A = 0.8. What is sin 2A?
Answer 0.96
Why 0.96.